[/quote]
,
such that: 
.
are non-negative integers.
doesn't have any solution on integers.
is strictly increasing : 
be a polynomial with real coefficients such that 
for all 
.
for some real constant 
and 
.
be a continuous function. A chord is defined as a segment of integer length, parallel to the x-axis, whose endpoints lie on the graph of 
.
chords, one of which has length 2025. Find the minimum possible value of 
.
for which 
is a perfect square.
be a hyperboloid of one sheet and let 
be another quadric that intersects the hyperboloid at the curve 
.
be a point on 
be a line through 
,
to be the line through 
.
then this is true for all initial choices of 
is a square. Prove that 
is not prime.
be a real polynomial of degree 
that has only simple roots. It is possible to determine a positive quantity 
so that for every pair of positive real numbers 
,
with 
,
has exactly 
or 
sign variations.
Y by
a) A positive integer is written at each vertex of a triangle. Then on each side of the triangle the greatest common divisor of its ends is written. It is possible that the numbers written on the sides be three consecutive integers, in some order?
b) A positive integer is written at each vertex of a tetrahedron. Then, on each edge of the tetrahedron is written the greatest common divisor of its ends . It is possible that the numbers written in the edges are six consecutive integers, in some order?
b) A positive integer is written at each vertex of a tetrahedron. Then, on each edge of the tetrahedron is written the greatest common divisor of its ends . It is possible that the numbers written in the edges are six consecutive integers, in some order?
